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Full text of "Analytical Mechanics"

WORK                                              17S
136.   Hooke's Law.  The relation which connects a stress with the strain which it produces is known as Hooke's law It states that stress is proportional to strain:
s=xs,                         (vr
where X is the constant of proportionality, and is called th( modulus of elasticity.
137.   Elastic Limit.  Hooke's law holds true so long as stress is small enough to leave no appreciable permanent deformation.    In other words, Hooke's law holds true strictly only while the body under consideration behaves like a perfectly elastic body under the action of the given stresses All bodies are more or less imperfectly elastic; that is, stresses always leave bodies with permanent strains.    Therefore ai the best Hooke's law is approximately true when appliec to material bodies.    The approximation, however, is close enough for practical purposes so long as the permanent deformation is negligible compared with the total deformatior produced by the stress.    If a considerable portion of th( deformation becomes permanent the body under stress is said to have reached its elastic limit, when Hooke's law does not give a close enough approximation and consequent!} cannot be used.
138.   Young's Modulus.  The modulus of elasticity of  body which is being stretched is called Young's modulus Let the body be an elastic string, a wire, or a rod, and let A be the area of its cross-section, L its natural or unstretchec length, and I the increase in length due to stretching.   Ther we have
c    P -A         l S = -7 and ==
A               L
nnv* /^-vwP/vf/i                                      = \ .